The phone lines to an airline reservation system are occupied 45% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that eight calls are placed to the airline. (a) What is the probability that for exactly two calls the lines are occupied

0.1569 = 15.69%

Step-by-step explanation:

If eight calls were placed, and we need to know the probability of exactly two calls were occupied, we need to calculate a combination of 8 choose 2 (all the combinations of 2 occupied calls in the 8 total calls), and multiply by the probability of each case in the 8 calls (2 cases occupied and 6 cases not occupied):

P (8,2) = C (8,2) * p (occupied) ^2 * p (not_occupied) ^6

P (8,2) = (8*7/2) * (0.45) ^2 * (0.55) ^6

P (8,2) = 28 * 0.2025 * 0.02768 = 0.1569 = 15.69%